What is covariance and what type of measurement is it?

Study for the Breeding and Genetics Exam 1. Sharpen your skills with engaging questions, hints, and detailed explanations. Master key concepts and prepare to excel.

Multiple Choice

What is covariance and what type of measurement is it?

Explanation:
Covariance measures how two traits vary together in a population. It is defined as the average product of each observation’s deviations from its respective mean: Cov(X,Y) = E[(X − μX)(Y − μY)]. In a sample, this is computed as (1/(n−1)) Σ (xi − x̄)(yi − ȳ). The sign shows direction: positive means high values of one trait tend to go with high values of the other, negative means they move in opposite directions. It’s a measure of joint variability, not a standardized relationship, so its magnitude depends on the units of X and Y. The correct description matches this as the average product of deviations from the means of two traits in the population. The other options describe variance of each trait, the correlation coefficient, or the mean of the two traits, which are not covariance.

Covariance measures how two traits vary together in a population. It is defined as the average product of each observation’s deviations from its respective mean: Cov(X,Y) = E[(X − μX)(Y − μY)]. In a sample, this is computed as (1/(n−1)) Σ (xi − x̄)(yi − ȳ). The sign shows direction: positive means high values of one trait tend to go with high values of the other, negative means they move in opposite directions. It’s a measure of joint variability, not a standardized relationship, so its magnitude depends on the units of X and Y. The correct description matches this as the average product of deviations from the means of two traits in the population. The other options describe variance of each trait, the correlation coefficient, or the mean of the two traits, which are not covariance.

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